Question

figure j k l m is a parallelogram. the measures of line segments m t and t k are shown. what is the value of y? 1 2 7 8

Explanation:

Step1: Use property of parallelogram diagonals

In a parallelogram, diagonals bisect each other. So \(MT = TK\).

Step2: Set up the equation

Given \(MT=8y + 18\) and \(TK = 12y-10\), we have the equation \(8y + 18=12y-10\).

Step3: Solve the equation for \(y\)

Subtract \(8y\) from both sides: \(18=12y - 8y-10\), which simplifies to \(18 = 4y-10\).
Add \(10\) to both sides: \(18 + 10=4y\), so \(28 = 4y\).
Divide both sides by \(4\): \(y=\frac{28}{4}=7\).

Answer:

\(7\) (corresponding to the third option)